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" If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively, to the triangles A'E'B',... "
Elements of Geometry and Trigonometry: With Notes - Σελίδα 75
των Adrien Marie Legendre - 1828 - 316 σελίδες
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 393 σελίδες
...the lengths of D'E' and E'C'. BOOK III.— SIMILAR FIGURES. Proposition 2 1 . Theorem. 320. If two polygons are composed of the same number of triangles similar each to each, and similarly placed, the polygons are similar. Hyp. Let the AS ABC, ACD, ADE of the polygon ABCDE be similar respectively...

Plane and Solid Geometry

Seth Thayer Stewart - 1891 - 406 σελίδες
...polygons may be divided into the same number of similar triangles, similarly placed. PROP. XIII. Polygons composed of the same number of triangles, similar each to each, and similarly placed, are similar. PROP. XIV. The perimeters of similar polygons are proportional to any homologous...

Elementary Geometry

William Chauvenet - 1893
...PROPOSITION V. Two triangles are similar when their homologous sides are proportional. PROPOSITION VI. If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. PROPOSITION VII. Two similar polygons may be decomposed into the...

Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - 1894 - 395 σελίδες
...draw a line parallel to one' of the given lines (Art. 226.) PROPOSITION XIX. THEOREM. * 236. // two polygons are com,posed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. Let the polygons AB CD EF and A' B' C' D E' F be composed of the...

Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - 1894 - 395 σελίδες
...and similarly placed, the polygons are similar. Let the polygons AB CD EF and A' B' C' D' E' F' be composed of the same number of triangles, similar each to each and similarly placed, ABC being similar to A' B' C ', and so on for the other triangles. To prove that the polygons...

An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - 1894 - 138 σελίδες
...Theorem. The homologous bases of similar triangles are to each other as their altitudes. 227. Theorem. Two similar polygons are composed of the same number of triangles, similar pair by pair, and similarly placed. 228. Theorem. Two polygons are similar if they are composed of...

Elements of Geometry: Plane and Solid

John Macnie - 1895 - 374 σελίδες
...those mutually parallel or perpendicular. PROPOSITION XVII. THEOREM. 294. Two polygons are similar if composed of the same number of triangles similar each to each and similarly placed. D ~4' Given: In polygons p and P', triangles AED, ADC, ACB, similar to triangles A'E'D', A'D'C',...

Syllabus of Geometry

George Albert Wentworth - 1896 - 50 σελίδες
...lines intercept proportional segments upon two parallels, they pass through a common point. 331. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. 332. If two polygons are similar, they are composed of the same number...

Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables

Joe Garner Estill - 1896 - 161 σελίδες
...Show how to inscribe in a given circle a regular polygon similar to a given regular polygon. 6. If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. The University of Chicago, September, 1896. TIME ALLOWED, ONE HOUR...

Plane Geometry

George D. Pettee - 1896 - 253 σελίδες
...AC = 36, what is the length of EC? Puoros1T1oN XVIII 210. Theorem. Two polygons are similar if they are composed of the same number of triangles similar each to each and similarly placed. Appl. Dem. Msim.N Psim. Q Rs'im.S Prove © sim. x = z Y = V C=3 AC^BC .LO & O 14} & G [in sim....




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